You're right - 4 inches deep could take forever for the vinegar to soak in. I use putty knives and screw drivers to pry the leg off by tapping them into the small opening - let the vinegar work - tap in a larger tool - little by little - more vinegar - bigger tool - The other option is after you create a hairline opening you could just saw off the leg without risking damage by twisting dry. SA

Injection of vinegar for disassembly would work better than injecting glue into a joint for repair. The dowels or mortise take up most of the space so even if you inject glue it won't coat the tenon or dowel that well but in a pinch it helps just not as good as taking the joint apart and cleaning off the old glue.

Here's one method for injection ......In the example for repairing a leg to a rail and the joint is held together by glue and two dowels. The joint is loose but can't be disassembled because of some stubborn glue, webbing, or fabric making disassembly not worth the effort. If you can estimate the thickness of the side rail before the dowel pocket than add 1/2 of 3/8ths the thickness of the dowel - so the center point of the dowel pocket is about 3/8ths deep on 3/4 lumber.

Now estimate the depth of the dowel into the rail and what you're looking for is that 1/4 - 3/8 inch space that's empty at the end of the pocket when the dowel is fully inserted. Mark a tiny 1/16th drill bit with a piece of tape at the 7/16th mark and drill a test hole (in the side of the rail that doesn't show if possible) to find that open space assuming the length of the dowel is approx. 1-1/2 inches deep. You will feel the drill bit lurch forward when t finds the empty space like drilling through sheet rock. When you have the right spot drill a slightly bigger hole up to 1/8 for your glue injector. Mixing a little water with the glue to make it more liquid. Inject until the glue backs out - plug the hole with a tiny dowel and clamp the joint tightly this should force glue like a piston around a portion of the dowel -

Sounds like a lot of trouble that way - and I'm guilty of taking my pneumatic brad nailer and just shooting through the dowels after clamping the joint. What matters to me is if it is an antique piece of something less quality SA